Volume Calculator
Calculate the volume of cube, rectangular prism, triangular prism, cylinder, sphere, hemisphere, cone and pyramid with step-by-step formulas.
This volume calculator finds the volume of a cube, rectangular prism, triangular prism, cylinder, sphere, hemisphere, cone and pyramid, showing the exact formula and step-by-step working for every shape. Whether you are filling a tank, pouring concrete, packing a box or solving a geometry homework problem, you enter the measurements and get an instant, accurate result in cubic units. It doubles as a dedicated cylinder, sphere, cube, cone and pyramid solver, all on one screen.
What Is Volume?
Volume is the amount of three-dimensional space a solid object occupies, or the capacity it can hold. While area measures a flat surface in square units, volume measures space in cubic units — cubic centimetres (cm³), cubic metres (m³) or litres. One litre equals exactly 1 cubic decimetre (1 dm³ = 1,000 cm³), which is why a volume calculator is the fastest way to convert a container's dimensions into the liquid capacity it can hold.
Volume Formulas for 3D Shapes
The table below lists every volume formula the calculator uses, with the inputs each shape needs and a worked example. Keep all your measurements in the same unit and the result will be correct every time.
| Shape | Volume Formula | Required | Example (cm³) |
|---|---|---|---|
| Cube | V = a³ | Side (a) | a=5 → 125 |
| Rectangular Prism | V = a × b × h | Length, width, height | 4×3×6 = 72 |
| Cylinder | V = π × r² × h | Radius (r), height (h) | r=5, h=10 → ≈785.4 |
| Sphere | V = (4/3) × π × r³ | Radius (r) | r=6 → ≈904.8 |
| Hemisphere | V = (2/3) × π × r³ | Radius (r) | r=4 → ≈134.0 |
| Cone | V = (1/3) × π × r² × h | Base radius (r), height (h) | r=3, h=9 → ≈84.8 |
| Pyramid | V = (1/3) × a × b × h | Base length, width, height | 6×4×9/3 = 72 |
| Triangular Prism | V = (a × h₁ / 2) × h₂ | Triangle base & height, prism height | (5×4/2)×8 = 80 |
How to Calculate the Volume of a Cylinder
To calculate the volume of a cylinder, square the radius, multiply by π, then multiply by the height: V = π × r² × h. A cylinder with a radius of 5 cm and a height of 10 cm has a volume of π × 25 × 10 ≈ 785.4 cm³. This is the formula you need for tanks, pipes, round containers, cans and silos, and the cylinder volume calculator tab applies it the moment you enter the two measurements.
How to Calculate the Volume of a Sphere
To calculate the volume of a sphere, cube the radius, multiply by π, then multiply by four-thirds: V = (4/3) × π × r³. A sphere with a radius of 6 cm has a volume of (4/3) × π × 216 ≈ 904.8 cm³. A hemisphere is exactly half of this, so the hemisphere volume calculator uses V = (2/3) × π × r³. Sphere volume is used for balls, domes, tanks and any rounded vessel.
Volume of a Cube and Rectangular Prism
The volume of a cube is the simplest of all: cube the side length, V = a³. A cube with a 5 cm side holds 125 cm³. The volume of a rectangular prism (a box) uses V = a × b × h — length times width times height. A box measuring 4 × 3 × 6 cm has a volume of 72 cm³. These are the most common everyday calculations, covering rooms, swimming pools, aquariums and shipping containers.
Volume of a Cone and Pyramid
A cone and a pyramid both taper to a point, so each holds exactly one-third of the prism that surrounds it. The volume of a cone is V = (1/3) × π × r² × h and the volume of a pyramid is V = (1/3) × base area × h. The cone volume calculator and pyramid volume calculator handle both, making short work of funnels, roofs, ice-cream cones and tent shapes.
Common Uses of a Volume Calculator
Knowing how to calculate volume quickly is useful far beyond the classroom. Typical real-world applications include:
- Liquid capacity: Find how many litres a tank, barrel or pool holds (1 litre = 1 dm³ = 1,000 cm³).
- Construction: Calculate concrete, fill material or excavation volume in cubic metres.
- Packaging & shipping: Determine how much product fits in a box or container and work out dimensional weight.
- Maths & school: Solve geometry problems for cylinder, sphere, cone, prism and pyramid with step-by-step formulas.
- Aquariums & pools: Estimate the water volume needed to fill a tank or pool to a given height.
For every shape the calculator displays the volume formula it used and the full substitution, so you not only get the answer but also see exactly how it was reached. Keeping every measurement in the same unit is the single most important step for an accurate result. For more worked examples, see the frequently asked questions below.
Frequently Asked Questions About the Volume Calculator
Cylinder volume: V = π × r² × h. A cylinder with radius 5 cm and height 10 cm has volume ≈ 785.4 cm³.
Sphere volume: V = (4/3) × π × r³. A sphere with radius 6 cm has volume ≈ 904.8 cm³.
Cube volume: V = a³. A cube with side 5 cm has volume 125 cm³.
Cone volume: V = (1/3) × π × r² × h. A cone with base radius 3 cm and height 9 cm has volume ≈ 84.8 cm³.
Rectangular prism volume: V = a × b × h. A box 4 cm × 3 cm × 6 cm has volume 72 cm³.
Cube: a³; Rectangular prism: a×b×h; Cylinder: π×r²×h; Sphere: (4/3)πr³; Hemisphere: (2/3)πr³; Cone: (1/3)πr²h; Pyramid: (1/3)×base×h; Triangular prism: (a×h₁/2)×h₂.
Couldn't find the answer you were looking for?
Explore all our tools and get the fastest answer to your question.